Because the problem of ranked retrieval is a problem of discriminant analysis, we have considered the problem from a nonparametric viewpoint as a problem in partition based regression. Maximum likelihood partitions are considered and we have been able to prove several limit theorems for the log likelihood ratio. These results lead to a more efficient cross-validation for optimal partition construction based on data. We have applied this method to study the scoring formulas developed in our latest retrieval model in order to test the optimality of the procedure for combining data to produce scores.